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Neorealism and the Internal Language of Topoi

Crudely formulated, the idea of neorealism, in the way that
Chris Isham and Andreas Doering use it, means that each theory of
physics, in its mathematical formulation should share certain structural
properties of classical physics. These properties are chosen to allow some degree of
realism in the interpretation (for example, physical variables always have values).
Apart from restricting the form of physical theories, neorealism does
increase freedom in the shape of physical theories in another
way. Theories of physics may be interpreted in other topoi than the category
of sets and functions.

In my talk I will concentrate on two topos models for quantum
theory. The contravariant model of Butterfield, Isham and Doering on the
one hand, and the covariant model of Heunen, Landsman and Spitters on the
other. I will argue that when we think of the topoi as generalized
categories of sets (i.e. when we use the internal perspective of the topoi at hand),
these two models are closely related, and both resemble classical physics.